High Turbulent Kinetic Energy Research Articles

Computational Fluid Dynamics as a Digital Tool for Enhancing Safety Uptake in Advanced Manufacturing Environments Within a Safe-by-Design Strategy.

In modern manufacturing environments, pollution management is critical as exposure to harmful substances can cause serious health issues. This study presents a two-stage computational fluid dynamic (CFD) model to estimate the distribution of pollutants in indoor production spaces. In the first stage, the Reynolds-averaged Navier-Stokes (RANS) method was used to simulate airflow and temperature. In the second stage, the Lagrangian method was applied for particle tracing. The model was applied to a theoretical acrylonitrile butadiene styrene (ABS) filament 3D printing process to evaluate the factors affecting the distribution of ultrafine particles (30 nm). Key parameters such as ventilation system effects, the presence of cooling fans and the print bed, and nozzle temperatures were considered. The results show that the highest flow velocities (1.97 × 10-6 m/s to 3.38 m/s) occur near the ventilation system's inlet and outlet, accompanied by regions of high turbulent kinetic energy (0.66 m2/s2). These conditions promote dynamic airflow, facilitating particulate removal by reducing stagnant zones prone to pollutant buildup. The effect of cooling fans and thermal sources was investigated, showing limited contribution on particle removal. These findings emphasize the importance of digital twins for better worker safety and air quality in 3D printing environments.

Three-dimensional evolution and turbulent kinetic energy transport of tip vortex from an elliptical hydrofoil

A non-cavitating tip vortex generated by an elliptical hydrofoil is investigated utilizing tomographic particle image velocimetry (TPIV). Focus is placed on its three-dimensional evolution over a relatively large streamwise region, as well as the transport process of turbulent kinetic energy (TKE). Based on the variations in vortex structure and related vortex properties, three main stages of tip vortex evolution can be identified: formation stage, persistence stage, and decay stage. The boundary between the formation and persistence stages is the position where tip vortex cavitation (TVC) is more prone to incept, attributed to the rapid growth in vortex circulation and vortex-center axial velocity, along with high turbulent fluctuations. During the tip vortex evolution, its swirling momentum significantly influences the axial flow pattern, likely by altering the pressure gradient along the vortex path. TKE transport equation is employed to analyze the turbulent properties of the tip vortex. Flow near the hydrofoil tip is highly turbulent and unsteady, with the local TKE at an excessive level. The local high TKE tends to diffuse into surrounding flow rather than being concentrated within the tip vortex as it moves downstream. TKE is mainly produced on the suction side of hydrofoil, potentially due to local boundary-layer behaviors, and is subsequently transported into the vortex core. As the tip vortex propagates further downstream, the in-core TKE exhibits a decreasing trend, and a relaminarization process appears to occur in far wake region. The flow topology of the tip vortex is examined with the invariants of velocity gradient tensor, providing insights into the topological features during the vortex evolution.

Toward High-Efficiency and Low-Emissions Hydrogen Direct Injection Internal Combustion Engine: Pre-Chamber Turbulent Jet Ignition

ABSTRACT Hydrogen internal combustion engine (HICE) holds significant promise for transitioning to clean fuels within the transportation field. This research investigates the adaptability of pre-chamber turbulent jet ignition (TJI) in direct injection (DI) HICE, focusing on addressing challenges such as reduced flame speed under lean-burn strategy and high NOx emissions during high-efficiency operation. Using a 3D CFD model of a DI HICE, we explore the impact of different ignition modes on mixing, combustion, and NOx emissions. Our findings reveal that the passive pre-chamber mode leads to a modest improvement in thermal efficiency and a reduction in NOx emissions compared to the spark ignition (SI) mode. In contrast, the active pre-chamber mode, characterized by a faster flame velocity, enhances indicated thermal efficiency (ITE) by about 2% compared to other ignition modes. We identify an optimal injection strategy for the pre-chamber, involving the injection of 0.3 mg of hydrogen. Deviations from this hydrogen quantity adversely reduce the thermal efficiency. Moreover, advancing injection timing promotes fuller mixing at higher turbulent kinetic energy, resulting in faster flame propagation albeit with a marginal rise in NOx emissions. Adjusting the equivalence ratio leads to an extension of the lean burn limit to the equivalence ratio of 0.25, while still achieving efficient combustion with ITE exceeding 49% at equivalence ratios of 0.3 or higher. Ultimately, we demonstrate the attainment of high-efficiency and low-emission combustion, with ITE surpassing 50% and NOx emissions falling below 80 ppm.

Study on the heat transfer deterioration of supercritical nitrogen in a vertical tube using a pseudo-boiling model

Heat transfer performance of supercritical cryogenic fluid plays a pivotal role in hypersonic vehicle engine cooling and cryogenic fuel vaporization. Heat transfer becomes highly complicated due to the complex physical properties of supercritical fluids (SFs). Heat transfer deterioration (HTD) occurs in SFs similar to the departure from nucleate boiling of subcritical fluids, resulting in a sudden temperature rise. In this study, a pseudo-boiling model is used to investigate HTD of supercritical nitrogen (SCN2) in vertical tubes. The distribution of the pseudo-vapor phase is analyzed to understand the heat transfer behavior in both normal heat transfer (NHT) and HTD regions. Simulation results show that the accumulated pseudo-vapor film weakens the heat transfer from the wall to the mainstream region, resulting in HTD. The critical heat flux (CHF) of SCN2 is observed in the simulation and verified by experimental data. Further investigation into buoyancy and thermal acceleration elucidates the absence of CHF under large mass flux conditions. The forced convection of high turbulent kinetic energy hinders the accumulation of pseudo-vapor film, resulting in NHT under large mass flux conditions. This paper provides a new approach and insights to investigate HTD of SFs using the pseudo-boiling model.

Experimental study of solid-liquid two-phase flow field in a centrifugal pump volute under multiple working conditions

In order to study the variation law of the solid-liquid two-phase flow field in the volute of centrifugal pump and the distribution law of the solid particles in the volute, based on PIV technology, the dynamic and static interference flow field of the volute under different flow conditions (30 m3/h, 40 m3/h, 50 m3/h, 60 m3/h, 70 m3/h) and different solid phase volume fractions (1 %, 1.5 %, 2 %) is studied. It is found that with the increase of the solid phase volume fraction, the head and efficiency of the centrifugal pump gradually decrease, and the addition of the solid phase has little effect on the pump head when the solid phase volume fraction is small under the condition of the large flow. The high turbulent kinetic energy area in the volute is mainly concentrated near the outer wall of the volute and the area where the tongue is located. Under the same solid phase volume fraction, the turbulent kinetic energy in the volute increases with the increase of the flow rate. The turbulent kinetic energy in the volute decreases with the increase of the solid phase volume fraction. The absolute velocity component of the flow field in the volute is significantly affected by the flow condition.

Can intense storms affect sinking particle dynamics after the North Atlantic spring bloom?

AbstractThe sinking of large particles (i.e., marine snow) has long been recognized as a key pathway for efficient particulate organic carbon (POC) export to the ocean interior during the decline of spring diatom blooms. Recent work has suggested that particles smaller than marine snow can also substantially contribute to POC export. However, a detailed characterization of small and large sinking particles at the end of blooms is missing. Here, we separately collected suspended and small and large sinking particles using Marine Snow Catchers and assessed their biogeochemical composition after the North Atlantic spring bloom in May 2021. During the 3 weeks of sampling, when four intense storms (maximum wind speeds 37–50 kt) created high turbulent kinetic energy dissipation rates and deepened the mixed layer, we observed two distinct sedimentation events. At first, sinking particles were dominated by small (diameter < 0.1 mm), slowly sinking ( 18 m d−1), particles rich in silica that carried a moderate POC flux (< 6 mmol C m−2 d−1) to 500 m depth. Once the storms ceased, the volume of large (diameter > 0.1 mm), fast‐sinking (> 75 m d−1), carbon‐rich marine snow aggregates (not fecal pellets) increased exponentially and POC fluxes at 100 m depth were more than fourfold greater (30 ± 12 mmol C m−2 d−1) than those during the previous event. The aggregates consisted of a mixed post‐bloom plankton community. Our data suggest that the storms shaped the timing, type, and magnitude of POC flux at the end of this spring phytoplankton bloom.

Experimental and numerical investigations into cold flow characteristics of multiple micro-mixing jets for hydrogen-rich gas turbines

To explore the flow field of micro-mixing jets, cold flow characteristics of a model Micromix burner were investigated by particle image velocimetry (PIV) system and Large-eddy simulation (LES) model. Results show that LES results are in good agreement with experimental results. In the flow field of multiple micro-mixing jets, the jet velocities of nozzles farther away from the burner center have a high increase and decay rate. When the outlet Reynolds number increases, the Reynolds stress increases first and then decreases in the merging region indicating that the velocity fluctuation disappears in the second jet half, but it has little effect on the flow field structure. Comparing the flow fields of round multiple micro-mixing jets, the merging point and combined point in the elliptical jets flow field move backward. Moreover, the maximum velocity for elliptical jets is also faster than the round jets, which is caused by the high turbulent kinetic energy in the elliptical jet flow field. When the tube spacing increases from 2 to 3 times the tube diameter, positions of the two feature points change linearly. Further, the surrounding jets can decrease the velocity attenuation of the center nozzle and elongate the axial length of the two feature regions.

Numerical Simulation Study of the Effect of Vegetation Cover on the Flow Characteristics of an Open Channel

ABSTRACTVegetation in rivers has a significant influence on flow characteristics. A numerical simulation was conducted to study the impact of different vegetation coverage on the flow characteristics in open channels, using ANSYS Fluent for a three‐dimensional computational fluid dynamics analysis. The results showed that as vegetation coverage increased, the water resistance effect was enhanced. In experiments with the same vegetation coverage, the group with more vegetation exhibited a more significant flow resistance effect. Additionally, as vegetation coverage increased, the turbulent kinetic energy also increased, with a range of 35.7%–82.5%. In experiments with the same vegetation coverage, the group with more vegetation had higher turbulent kinetic energy, with an increase ranging from 39.8% to 69.8%.

The Influence of the Intake Geometry on the Performance of a Four-Stroke SI Engine for Aeronautical Applications

In this work, the influence of plenum and port geometry on the performance of the intake process in a four-stroke spark ignition engine for ultralight aircraft applications is analyzed. Three intake systems are considered: the so-called “standard plenum”, with a relatively small plenum volume, the “V1 plenum”, with a larger plenum volume, and the “standard plenum” equipped with a large curvature manifold called the “G2 port”. Both measurements and 3D CFD simulations, by using Ansys® Academic Fluent, Release 20.2, are performed to characterize and analyze the steady-flow field in the intake system for selected valve lifts. The experimental data and the numerical results are in excellent agreement with each other. The results show that at the maximum valve lift, i.e., 12 mm, the V1 plenum allows an increase in the air mass flow rate of 9.1% and 9.4% compared to the standard plenum and the standard plenum with the “G2 port”, respectively. In addition, the volumetric efficiency has been estimated under unsteady-flow conditions for all geometries at relatively high engine rpms. The difference between numerical results and measurements is less than 1% for the standard plenum, thus proving the accuracy of the model, which is then used to study the other configurations. The V1 plenum shows a fairly constant volumetric efficiency as the engine speed increases, although such an efficiency is lower than that of the other two geometries considered in this work. Specifically, the use of the “G2 port” leads to an increase of 1.5% in terms of volumetric efficiency with respect to the configuration with the original manifold. Furthermore, for the “G2 port” configuration, higher turbulent kinetic energy and higher swirl and tumble ratios are observed. This is expected to result in an improvement of air–fuel mixing and flame propagation.

Experimental control of the flow separation behind a backward facing step using deep reinforcement learning

In this experimental study, a value-based reinforcement learning algorithm (deep Q-network, DQN) is used to control the flow separation behind a backward facing step at a Reynolds number of 2.9 × 104. The flow is forced by a dielectric barrier discharge (DBD) plasma actuator pasted at the upstream of the step edge, and the feedback information of the separation zone is provided by a hotwire sensor submerged in the downstream shear layer. The control law represented by a deep neural network is implemented on a field programable gate array (FPGA), able to execute in real-time at a frequency as high as 1000 Hz. Results show that both open-loop periodical control and DQN control can effectively reduce the reattachment length and the recirculation area. Compared with the former, which requires dozens of trail-and-error measurements lasting for hours, the latter is able to find an optimal control law in only two minutes, achieving a long-term reward 7% higher. Moreover, by introducing a weak penalty term for plasma actuation, the mean actuator power consumption in DQN can be cut down to only 60% of that in the optimal open-loop control, meanwhile sacrificing a negligible amount of control effectiveness. Physically, the open-loop periodical control destabilizes the shear layer earlier, increasing both the area and the peak amplitude of the high turbulent kinetic energy (TKE) zone, whereas under DQN control, only a slight increase in the TKE peak is observed, and the overall spatial distribution remains the same as baseline.

Experimental and numerical studies on the hydraulic performance and the internal flow characteristics of lead-bismuth in the main coolant pump of LFR

As the key component of the primary circuit of a lead-cooled fast reactor (LFR), the hydraulic performance and the internal flow characteristics of the main coolant pump (MCP) are significantly important to the long-term safe and efficient operation of LFR. The present study reports an experimental and numerical investigation of the hydraulic performance and the internal flow characteristics of a centrifugal pump, which is considered one of the candidates for the MCP in LFR. Based on the experimental platform of Liquid Metal-Supercritical Fluid coupled heat transfer (LMSF) of Xi’an Jiaotong University, the hydraulic performances of a centrifugal pump like the pump head and its efficiency are studied and the measured data is also used to validate the accuracy of the numerical method which are employed to study the flow characteristics of MCP, as velocity, pressure, turbulent kinetic energy (TKE). The results show that the deviation of experimental and numerical simulation results is less than 5%. The high velocity region in the impeller channel is concentrated near the hub side of the blade inlet, and the significant pressure difference of the blade surface is primarily concentrated in the second half and shroud region. The inlet area of the blade exhibits a concentration of high TKE and the circular distribution of TKE within the impeller exhibits a periodic pattern, with its frequency being consistent with the number of blades.

A variable turbulent Schmidt number model in Jet-in-Crossflow simulation and its applications

This study proposes a variable turbulent Schmidt number (Sct) model to improve the precision of Reynolds-Averaged Navier-Stokes (RANS) simulations for Jet-in-Crossflow (JICF) scalar mixing phenomena, with a particular focus on hydrogen/air mixing characterized by strong density variations. By incorporating a correction term associated with turbulent kinetic energy based on a selected Sct value, the model aims to amplify the diffusion rate of the jet, particularly in regions where the interaction between the mainstream flow and the jet is significant. This enhancement in simulation accuracy is validated against Large Eddy Simulation (LES) results, which serve as the benchmark for analysis. Statistical analysis of LES results reveals a notable increase in the turbulent diffusion coefficient in regions characterized by strong interactions between the jet and mainstream flow. Meanwhile, minimal variation in turbulent viscosity is observed, resulting in a reduced Sct in areas with high turbulent kinetic energy. The proposed model is validated within a open-space JICF case, a micro-tube JICF case and a free jet case. In micro-tube JICF scenarios, initial simulations with a fixed Sct value were conducted. Following comparison, a value of 0.7 was identified as the basis for correction. Subsequently, the variable Sct model was implemented, thereby enhancing the accuracy of RANS simulations in micro-tubes.

Numerical prediction of passive speed and performance for multistage pump without power drive in natural flow process

With the development of engineering applications and the increase in system complexity, some particular fields, such as liquid rocket engine turbopumps, aircraft engine fuel systems, and marine natural flow cooling systems, are increasingly focusing on the performance characteristics of pumps under natural flow conditions. The pump is in the form of resistance components under natural flow conditions without a power drive. The impeller undergoes passive rotation by the impact of inlet flow. Due to the specificity of its operating conditions and performance indicators, the pump's natural flow performance cannot be evaluated by regular methods. Therefore, this paper proposed a numerical prediction method for pump natural flow performance based on a coupled computational fluid dynamics coupled with six-degrees-of freedom model. The performance of a multistage pump with guide vanes was evaluated under different natural flow conditions, and the accuracy was verified by experimental measurements. The transient variation mode of pump performance parameters with time at the initial stage of natural flow impact was analyzed. The flow field's transient evolution characteristics and the wall shear stress variation during natural flow were investigated. It was found that the impeller's passive rotational speed increases linearly with the natural flow rate, while the hydraulic loss shows an exponentially increasing trend. Meanwhile, the natural flow loss coefficient shows an exponentially decreasing trend and gradually tends to a stable value. The high turbulent kinetic energy inside the impeller is mainly distributed in the flow separation region and large velocity gradients. The distribution of shear stresses is closely related to the flow behavior inside the pump and the geometrical features of the hydraulic components.

Numerical investigation of bimodal tip clearance effect on the lift-drag and flow characteristics of a hydrofoil

Tip leakage flow has adverse effect on energy conversion of the hydraulic machinery. The new tip clearance structure based on Bimodal Gaussian function is designed to reduce tip leakage vortex. The effects of bimodal structure with different amplitudes and arrangement positions on lift-drag and flow characteristics are studied. The results show that the maximum rise of the lift-drag ratio reaches 5.88% when the bimodal structure amplitude is equal to the tip clearance size. The bimodal structure reduces the outflow velocity at the peak and forms a smooth streamline, which weakens the entrainment with the mainstream. The location of the bimodal structure far away from leading edge helps to produce smooth streamlines and make the flow field smoother, and reduces the area of high turbulent kinetic energy region near leading edge and in tip clearance outflow region significantly. The arrangement position of bimodal structure close to leading edge can produce a low-speed zone or a recirculation zone in the mainstream, which can block the mainstream flow and reduce the energy characteristics of the hydrofoil.

Numerical investigation of particle behavior and erosion wear in a centrifugal pump using coarse-grained Discrete Element Method

Erosion wear presents a significant challenge in the operation of hydrodynamic systems, particularly in centrifugal pumps. To address this issue, this study employs the coarse-grained Discrete Element Method (CGDEM) coupled with Computational Fluid Dynamics (CFD) to predict erosion wear areas and elucidate particle behavior dynamics. The simulation considers spherical solid particles (brown corundum) with diameters ranging from 0.3 mm to 1 mm and volume fractions of 15% and 5%. The flow field is calculated using the Navier-Stokes equations and the shear-stress-transport (SST) k-ω model. Particle movement is tracked using Newton’s second law, considering drag and gravitational forces. Results indicate that the highest turbulent kinetic energy (TKE) occurs at a flow rate of Q = 15 m3/h. Moreover, the pressure reduces slightly when the flow rate increases, although flow velocity might increase with volumetric discharge. Additionally, increased particle diameter leads to greater erosion wear, particularly on blade leading edges, the volute tongue area, and the volute casing belly region. As particle mass concentration intensifies, wear rates on the volute wall and inner hub edge also increase. The study’s robustness is demonstrated through alignment between experimental and numerical data. This investigation offers valuable insights into erosion dynamics in centrifugal pumps, crucial for enhancing operational efficiency and mitigating erosion-induced challenges in these critical systems.

The influence mechanism of the submerged dikes on the three-dimensional hydrodynamic characteristics at the 90° confluence

The confluence area serves as the pivotal control unit in natural rivers, and the implementation of spur dikes at the confluence enables regulation of flow patterns, influences pollutant mixing, and safeguards against river scouring. This study establishes a three-dimensional hydrodynamic model for the 90° confluence with dikes, aiming to explore the impact of the number, angle, and spacing of the dikes on hydrodynamic characteristics at 90° confluence. The results show that (i) the closer the spacing between the dikes, the wider the range of low water level area upstream becomes. An increased number of dikes makes it easier for the downstream water level to recover. (ii) The area of the high turbulent kinetic energy region increases with the increase in the number of dikes. Among the three angle deployments, the dike deployment angle of 60° corresponds to the largest area of high turbulent kinetic energy. When the spacing between dikes is 0.225 m, it results in the largest area of high turbulent kinetic energy. (iii) The number or spacing of dikes exhibits a negative correlation with the shape parameters of the separation and backflow behind the dikes, whereas there is a positive correlation between the angle of dikes and these shape parameters. (iv) Influenced by the deployment of dikes, novel helical flows will be generated around the dikes at the confluence. The helicity of the clockwise helical flow is comparatively smaller than that of its counterclockwise counterpart. Subsequently, newly generated helical flows undergo fusion and division as it progresses downstream.

Flow Analysis of Central Venous Outflow Tract: A New Approach to Understanding Pulse-Synchronous Tinnitus.

Pulse-synchronous tinnitus (PST) has been linked to multiple anatomical variants of the central venous outflow tract (CVOT) including sigmoid sinus (SS) dehiscence and diverticulum. This study investigates flow turbulence, pressure, and wall shear stress along the CVOT and proposes a mechanism that results in SS dehiscence and PST. Case series. Tertiary Academic Center. Venous models were reconstructed from computed tomography scans of 3 patients with unilateral PST. Two models for each patient are obtained: a symptomatic and contralateral asymptomatic side. A turbulent model-enabled commercial flow solver was used to simulate the pulsatile blood flow over the cardiac cycle through the models. Fluid flow through the transverse and SS junction was analyzed to observe the velocity, pressure, turbulent kinetic energy (TKE), and shear stress over a simulated cardiac cycle. Fluid flow on the symptomatic side showed increased vorticity in the presence of an SS diverticulum. Higher TKE with periodicity following the cardiac cycle was observed on the symptomatic side, and a sharp increase was observed if SS diverticulum was present. Shear stress was highest near the narrowest segments of the vessel. Pressure was observed to be lower on the symptomatic side at the transverse-SS junction for all 3 patients. Computational fluid dynamics modeling of blood flow through the CVOT in PST suggests that low pressure may be the cause of dehiscence, and tinnitus may result from periodic increases in TKE.

A CFD Study on Optimization of Mass Transfer and Light Distribution in a Photocatalytic Reactor with Immobilized Photocatalyst on Spheres

This study explores the influence of flow velocity, sphere size, and inter-sphere distance on hydrodynamics and mass transfer in a photocatalytic reactor. The effects of two different light configurations on light distribution and degradation were also evaluated. A 2D computational fluid dynamics (CFD) model was developed to simulate the continuous flow photocatalytic reactor with TiO2-coated spheres and validated with experimental measurements by observing the degradation of methyl orange. The experimental setup consists of a tube containing an equal number of TiO2-coated glass spheres. The case with radiation from one wall shows a non-uniform light distribution compared with the case with radiation from both walls. The CFD simulations focused on analyzing the velocity streamlines and turbulence characteristics (turbulent kinetic energy (TKE) and turbulence dissipation rate (TDR)). These parameters showed significant variations in each studied case. The case with larger spheres reached the highest velocity of 38 m/s of the pollutant solution. The highest TKE and TDR values of 0.47 m2/s2 and 12.2 m2/s2, respectively, were also observed in the same case, indicating enhanced mixing and mass transfer to the catalyst surfaces, ultimately leading to a more efficient degradation process. The results show that an optimized design of photocatalytic reactors can significantly improve mass transfer and, thus, degradation efficiency.

Large eddy simulation study on drag reduction performance of array-based plasma synthetic jet actuators

Large Eddy Simulation (LES) is first used to investigate the drag reduction effect of an array-based configuration of Plasma Synthetic Jet Actuators (PSJAs) on a hemisphere in supersonic inflow, and analyze the effect of energy allocation and array angle on the drag reduction performance of opposing Plasma Synthetic Jet (PSJ) in this paper. Numerical simulation results have been compared with experimental data, confirming the validity of the simulation method. The results show that different energy allocations have a significant effect on the drag of the hemisphere. However, the effect of the change in array angle on the drag of the hemisphere is not as noticeable as the effect caused by energy allocation. Interference regions between the two PSJAs occur, which undermine the effectiveness of drag reduction. High Turbulent Kinetic Energy (TKE) regions primarily concentrate on the core region of the jet and downstream of the bow shock. The influence of the array angle on TKE is most evident in the downstream region of the exits of the PSJs on both sides. Temporal evolution of the coherent structures reveals that as the PSJ intensity decreases, the large-scale vortices progressively break up into smaller-scale vortices, and energy is also transferred from large-scale structures to small-scale structures.

Numerical analysis of the transient characteristics of internal flow in the acceleration process of variable speed regulation of a centrifugal pump

Abstract In this study, a method of combining Flowmaster and ANSYS CFX software was adopted. Based on the consistency between the numerical calculation results of the hydraulic performance of a centrifugal pump and the test results, an operating model of a centrifugal pump system is established, variation law of the external characteristic parameters in the transient process is obtained, and different acceleration times and modes are set. The change law of the transient external characteristics and the evolution mechanism of the internal flow field during the variable speed regulation and acceleration of the centrifugal pump are disclosed. By introducing a control system evaluation index, the effects of acceleration time and mode on performance and internal flow field of variable speed control process of the centrifugal pump are analysed in detail. The results show that the turbulent kinetic energy in the pump changes violently, and the high turbulent kinetic energy and high vorticity are widely distributed, which has an obvious transient effect. An exponential acceleration method can effectively reduce the peak value and overshoot of external characteristic parameters while reducing the speed regulation time.